Baker Kearfott wrote:
Ah, yes, now I remember. Even though we are working only
with real numbers, an interval can be bounded or not,
and we can distinguish that with a decoration. However,
a consequence of the fact we interpret [a,Infinity) to
be a set of real numbers is [a,Infinity)*0 = 0. Thus,
the question of the point product Infinity*0 does not
even arise.
Right.
...although it _does_ arise when computing the endpoints of an interval.
So it is relevant to the _implementation_ of interval arithmetic
operations. I think this was Ian's main point (no pun intended).
For example, _if_ IEEE 754 had made a distinction between Infinity and
Overflow, then our interval arithmetic implementations would already
have a fast floating-point operation Overflow*0=0 in hardware, which
means computing the appropriate interval endpoint of the product:
[1,Overflow]*[0,0]=[1*0,Overflow*0]=[0,0]
would already be performed fast and cheaply in hardware.
This would be good for all of our (currently slow) software
implementations of interval arithmetic.
This is in contrast to how IEEE 754 arithmetic hardware as it _actually_
exists today yields:
[1,Infinity]*[0,0]=[1*0,Infinity*0]=[0,NaN]
which according to Motion 5 is not the correct interval result. So it
requires an expensive software routine to "fix" the [0,NaN] result and
turn it into the correct [0,0] interval arithmetic result.